Bodies in the water were a job for the Water Police. But sometimes they would push the body onto the shore and call for the regular cops. And they would nudge it back into the water. Nobody wanted to touch a body that was floating, as it would have been in the water for a few days, was awfully smelly, and the new home for a bunch of sea critters.
I never did a night search for a report of a body, though we would go out if it was a plane going down or a mayday from a boat. Otherwise, a body didn't need urgent attention unless it was likely to drift away and sink again.